If you wore a condom, and it stayed intact, there's no reason to question your negative test results. Condoms prevent chlamydia transmission.
Oral sex can transmit chlamydia. How often is in question. We used to think it wasn't found in the throat, but are finding more of it now, and aren't sure if it's better testing or something else.
It's definitely less of a risk than vaginal or anal sex, but there is still a chance.
There is no risk from handjobs.
There is no risk if your penis touches her vulva (her vaginal lips). You need to penetrate her in order to get chlamydia.
If you are concerned about your doctor's organization, you can go to Planned Parenthood for testing, or a local STD clinic. You can also use an online testing site, like STDCheck.com, letsgetchecked.com, ultalabtests.com.
They all run specials all the time, and you can search Google for coupon codes.
Gonorrhea is also a possibility from oral sex - more common from oral than chlamydia is.